# Unit4 Laplace Transform in network analysis and synthesis- Btech AKTU

Discussing some Important Questions in network analysis and synthesis Unit 4 Laplace Transform. I hope that these crucial questions will be useful to you in your next Btech AKTU exams.

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## Q. Discuss briefly singularity functions.

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1. Singularity functions are particular forcing functions that are discontinuous or have derivatives that are discontinuous.

2. The commonly used singularity functions are:

• Step function
• Ramp function
• Impulse function

Unit step (Step function): Signals which start at time t = 0 and have

magnitudes of unity are called unit step signals.

They are represented by a unit step function u(t).

They are defined mathematically as:

Unit ramp (Ramp function) : Unit ramp signals are defined as signals that begin at zero and are linear in nature with a constant slope m.

They are represented by a unit ramp function r(t).

They are defined mathematically as:

Unit impulse (Impulse function) : Signals which act for very small time but have large amplitude are called unit impulse functions.

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## Q. Discuss the step response of the series RLC network.

Ans. 1. Fig. 4.23.1 shows a network consisting of resistance (R), capacitance (C) and inductance (L) are connected in series.

2. It is provided with a switch as shown in Fig. 4.23.1. Initially switch was kept open. Switch was closed at t =0.

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